We know you've heard it before: Racial bias infuses our criminal-justice system on every level, from initial arrests to decisions about sentencing.

But Freakonomics is reporting on a new study of capital sentences handed down in first-degree murder cases that takes a slightly different twist. It focuses on the relationship between the races of defendants and victims and the reversal of capital sentences by higher courts (in the U.S., all first-degree capital sentences are automatically appealed).

The study (abstract here, pdf here; conducted by Harvard economist Alberto Alesina and Eliana La Ferrara of Università Bocconi) finds that initial sentences handed down to minority defendants convicted of killing white victims were as much as 9 percent more likely to involve errors that had to be reversed by higher courts than were those in cases involving a minority defendant killing a minority victim.

The study's authors pinned their results on the assumption that superior courts can only improve on the accuracy of first sentencing and therefore remove part or all racial bias.

A summary of the results:

When we implement our test we find results consistent with the presence of racial prejudice: ceteris paribus, first degree courts are more severe (i.e., they tend to give more death sentences which are then reversed) against cases involving a minority defendant killing one or more white victims.

This result holds strong both for the cases that reach the final stage of revisions and appeal, the Habeas Corpus stage in Federal Courts, and for the full sample of cases in the first appeal stage, called Direct Appeal.

For Habeas Corpus cases involving a minority defendant, the error rate was 37.5 percent if the victim was white, and 28.4 percent if it was not white, with a statistically significant difference of 9 percentage points.

For cases involving a white defendant the difference indicates higher reversal rates when the victim is non-white, but it is not significant. In the Direct Appeal sample, cases involving a minority defendant had an error rate of 37.7 percent if the victim was white and 34.7 percent if the victim was a minority, with a statistically significant difference of 3 percentage points. In cases involving a white defendant the difference is again in the opposite direction and not significant. This pattern of results is consistent with racial bias according to our rank order test.